Arsène Wenger has promised to make a move in the January transfer market to plug the defensive gap in his Arsenal squad that he admits was there when the summer window closed.

The manager submitted a squad to the Premier League on 2 September that featured only five senior defenders, plus the 19-year-old Calum Chambers who joined from Southampton in July. Wenger also signed Mathieu Debuchy from Newcastle United as he looked to strengthen after the departures of Bacary Sagna and Thomas Vermaelen to Manchester City and Barcelona respectively.

Wenger, though, wanted another defensive player, ideally one who could cover in central defence and holding midfield. Debuchy is now a long-term casualty with ankle damage while Laurent Koscielny is out with tendinitis in his achilles and, to deepen Wenger’s headache before Saturday’s Premier League visit of Hull City, Chambers is suspended for the five yellow cards that he has collected in domestic competition. It is likely the left-back Nacho Monreal will have to fill in alongside Per Mertesacker at centre-half.

“I agree we could have bought one more player,” Wenger said. “We didn’t find [him]. We will try in December to rectify that because we are a bit short with the injuries we have and, overall, I think we will rectify that on the transfer market in January.”

Wenger was talking at the 13th Arsenal AGM, at which one of the key questions for shareholders was whether money had been made available for the purchase of the extra defender in the summer. According to the accounts, the club have £207.9m in the bank. But the chief executive, Ivan Gazidis, sought to debunk the perception that the board of directors, or Wenger, were sitting on “a huge cash pile” that they refused to spend.

Gazidis pointed out that the financial year-end of 31 May represented the “high point” of the year “when season-ticket and many sponsorship receipts have already been collected”. He broke down the headline figure, saying the “vast majority” of it had already been accounted for.

“We have committed a net £53m on new transfers since the May 31st date,” Gazidis said. “We have got liabilities of £29m still to pay on previous transfers and there is a further £17m of performance-related costs that we expect to have to pay on top of that. So that’s £99m of the published figure of £207.9m, which leaves us with £108.9m left.

“We have to keep a substantial amount of cash in reserve at all times in order to comply with our debt obligations and most of the remaining cash after that is needed to run the club across a full season, with all of the costs, including player salaries, associated with that. We also do some complex modelling forward over a number of years to work out that we can meet our anticipated financial commitments.

“We do try to keep a reasonable amount of cash available for further investment in the team. We don’t want to disclose that publicly because it’s obviously commercially and competitively sensitive but I’m afraid it’s nowhere near the numbers that are quoted and which fuel some degree of dissatisfaction. It’s quite untrue to suggest that the club is sitting on a huge cash pile that, for some unspecified reason, it refuses to use.”

The meeting was a stage-managed affair, although one shareholder did succeed in putting the board on the spot with the direct question about whether Wenger had the money to spend on the extra defender. His efforts were met with applause from the floor. But Sir Chips Keswick, the chairman, performed the final, verbal swerve of the day.

“I don’t think that it’s my wish or intention to double-guess what Arsène Wenger wants to do,” Keswick said. “As you know, your board backs him 100%. If he has a plan, we back him. If he doesn’t have a plan, we keep quiet. So don’t let’s be in a muddle about who calls the shots about football. It is not the chairman, it is not the fans, it is Mr Arsène Wenger.”

Keswick then turned to Wenger. “Arsène, I have embarrassed you. Do you wish to say anything else?” he said.

“No,” Wenger replied.

Keswick had earlier dodged the pre-submitted question that asked the board to explain how Stan Kroenke, the majority shareholder, had taken £3m out of the club in consultancy fees. The nature of the consulting work remains a mystery.

“This fee was proposed by myself and Lord Harris [the director] for the wide range of services provided to Arsenal Football Club by Kroenke Sports and Entertainment,” Keswick said. “KSE is one of the most respected and successful sports organisations in the United States, operating in the most sophisticated sports business market in the world.

“They have an extensive and long experience in modern sports management. It is of the utmost importance that we, as a club, use it to our best advantage to ensure we keep progressing. There was no competitive tender for these services as they are directly available to us and a tender process was unnecessary. We are entirely satisfied that this fee was appropriate. In terms of any future fees, that will depend on the nature of the services provided.”